The present invention relates to electronic devices, and, more particularly, to semiconductor circuits and methods useful for filtering digital data streams.
Digital Systems with Half-Band Filtering
Communications systems, such as broadcast radio, use frequency division multiplexing (FDM) to simulaneously transmit differing information signals from several sources in a single locale. Typically, each source modulates its carrier frequency with its information signal and keeps within its allocated frequency band. Extraction of a desired information signal from a received broadband of simultaneous broadcasts may be performed by mixing down (down conversion by the selected carrier frequency) followed by lowpass filtering and demodulation as schematically illustrated by system 100 in FIG. 1. Indeed, system 100 receives radio frequency signals (e.g., 100-200 MHz) at antenna 102, filters and mixes the signals down to intermediate frequencies (e.g., 1-10 MHz) with a wideband tuner 104, converts from analog to digital format with sampling analog-to-digital converter 106, extracts the selected frequency band (e.g., of width 5 KHz) with digital down converter 108 which performs the down conversion and filtering, and demodulates and reconstructs an analog information signal with demodulator/processor 110. For example, if wideband tuner 104 has a 10 MHz output bandwidth, then analog-to-digital converter 106 will sample at 20 MHz or more (at least the Nyquist rate), and digital down converter 108 will output a 5 KHz selected band at a sampling rate of 10 KHz. That is, digital down converter 108 may decrease the sampling rate due to the small bandwidth of its output without loss of information.
The problems of construction of system 100 include realizing digital down converter 108 operating at a high sampling frequency while maintaining a low ripple sharp cutoff filter which has programmable down conversion frequency and programmable bandwidth. Known realizations of a down conversion function include the combination of a numerically controlled oscillator/modulator (NCOM) such as the HSP45106 manufactured by Harris Corporation together with two decimating lowpass digital filters (one for the in-phase and one for the quadrature outputs of the NCOM) such as the HSP43220 also manufactured by Harris Corporation.
A lowpass decimating filter having a decimation rate R which may be factored as EQU R=R.sub.1 R.sub.2 . . . R.sub.M
may be realized as M cascaded independent lowpass decimation filters with the jth filter having decimation rate R.sub.j. This multistage approach may greatly reduce the number of computations required to perform the filtering. Indeed, the first stages in a multistage filter need not have narrow transition bands because the transition band of the last stage will essentially determine the overall transition band. Further, the early stages decimate the sampling rate so the latter stages operate at a much lower sampling frequency.
Multistage filters may be effectively designed with stages of half-band filters. A lowpass digital FIR filter with optimal (equiripple) design and with symmetry about .pi./2 is called a half-band filter. That is, a half-band filter has a transfer function Fourier transform as shown in FIG. 2a with passband and stopband of equal width. Half-band filters have about one half of their filter coefficients equal to zero, so the filter computations include only about one half as many multiplications as a usual FIR filter.
Half-band filters may appropriately be used only for decimation or interpolation of sampling rate by a factor of 2 and when aliasing to the final transition band is permitted. See FIG. 2b illustrating the aliasing of a decimation by 2 half-band filter. Thus multistage filters with powers of 2 decimation or interpolation profitably employ cascaded half-band filters.
Crochiere and Rabiner, Multirate Digital Signal Processing (Prentice-Hall 1983) provides general information regarding signal processing using sampling rate changes. Hogenauer, An Economical Class of Digital Filters for Deeimation and Interpolation, 29 IEEE Tr.Ac.Sp.Sig.Proc. 155 (1981) discloses decimation filters made of an integrator section followed by comb section operating a low sampling rate.
Features
The present invention provides a digital half-band filter with truncated multipliers and joint overflow and saturation compensating complementers. The truncated multipliers reduce the amount of hardware, and the complementers permit full dynamic range